A function gives every input exactly one output. These free printable worksheets ask whether a set of pairs or a table does that.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
The rule is one sentence long, which is why it needs a sheet: it is easy to recite and easy to apply backwards. A repeated OUTPUT is fine — (1, 3) (2, 5) (4, 5) is a function, and so is a flat day where every hour reads the same temperature. A repeated INPUT is what breaks it, and only when the two pairs disagree. A child who has heard "no repeats" remembers the ban without the half of the sentence that says which column it applies to.
So every sheet here carries relations that repeat an output and are still functions, sitting beside relations that repeat an input and are not. That is deliberate: a page whose only repeated numbers are the illegal ones can be cleared by hunting for duplicates, which tests eyesight rather than the definition. Roughly half the relations that repeat a number are functions.
One question from this sheet, worked through a step at a time.
x: 11, 11, 22, 8 y: 32, 31, 26, 7